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It seems to me that this is a series of rules for a game that would ALLOW Black to continue copying White's moves indefinitely. However, Black could break out at any time that White made what Black thought a bad move. Not having check is a problem, but I can think of a solution to that problem: still have check if ONE King is threatened, but not if BOTH are. Another rule would seem to be that no piece could cross the border of ranks 4 and 5 orthogonally, effectively making Rooks riverbound and forcing Pawns to capture in order to cross. In fact as this would eliminate the only symmetry-breaking captures, no other captures would need to be disallowed.